The length constant can be defined as: where rm is the membrane resistance (the force that impedes the flow of electric current from the outside of the membrane to the inside, and vice versa), ri is the axial resistance (the force that impedes current flow through the axoplasm, parallel to the membrane), and ro is the extracellular resistance (the force that impedes current flow through the extracellular fluid, parallel to the membrane).
[1] In calculation, the effects of ro are negligible,[1] so the equation is typically expressed as: The membrane resistance is a function of the number of open ion channels, and the axial resistance is generally a function of the diameter of the axon.
The length constant is used to describe the rise of potential difference across the membrane The fall of voltage can be expressed as: Where voltage, V, is measured in millivolts, x is distance from the start of the potential (in millimeters), and λ is the length constant (in millimeters).
Vmax is defined as the maximum voltage attained in the action potential, where: where rm is the resistance across the membrane and I is the current flow.
This means that the length constant is the distance at which 63% of Vmax has been reached during the rise of voltage.